826 



SCIENCE 



[N. S. Vol. XLI. No. 1066 



our measure of force from some phenomenon 

 more closely related to tlie concept. What we 

 are conscious of when we lift a pound weight is 

 not the am.ouiit of matter in it, but the force 

 upon it. 



If this sound reasoning is to be applied to all 

 the concepts of mechanics it wiU be necessary 

 to modify most of the equations slightly by 

 introducing a proportionality factor. This 

 has already been suggested by Professor 

 Hoskins in a footnote to his review of Maurer's 

 " Technical Mechanics," ^ but he failed to make 

 the most of his opportunity. We present here 

 a tentative scheme only and the calculated 

 values of a few of the constants. Our choice 

 of fundamental units of velocity and accelera- 

 tion are, we freely admit, open to the criticism 

 of being ill-considered and ofE-hand. Still they 

 will do perfectly well to illustrate the method, 

 and certainly they are much better than the 

 units in common use which only tend to cloud 

 the physical entity and reality of the magni- 

 tude in question by reference to others more 

 or less closely related. WTio that has con- 

 sidered with any care his sensations of a pass- 

 ing express train does not realize that his im- 

 pressions on the subject " how fast " are much 

 more direct and elemental than any question 

 of " how far " or " for how long " ? 



We begin then with the units of force, dis- 

 tance, time, quantity of matter and accelera- 

 tion as defined above and which for our present 

 purpose may be regarded as sufficiently un- 

 related to be called independent, fundamental 

 units. What definite velocity does nature pre- 

 sent to us that we may take as unity? After 

 considering the peripheral and the orbital 

 velocity of the earth and the maximum attain- 

 able velocity due to terrestrial gravitation 

 (that of a body falling from the hypothetical 

 "infinite distance"), it seemed well to aban- 

 don such gravitational velocities as being dan- 

 gerously near to our definition of unit force 

 (a totally unrelated concept) and adopt the 

 velocity of light, which is one of the most 

 definite and unalterable things in nature. This 

 unit we call the " speedal," not from, any wish 

 to be bizarre, but merely because some name is 

 1 Science, December 4, 1914. 



necessary to show where the idea leads us. 

 10"'' speedals we will call a micro-speedal. We 

 see no real objection to calling it pounds, 

 since we already employ this useful word to 

 designate unit quantity of matter and unit 

 force, but perhaps the present name will serve 

 our purpose better. 



Let W = quantity of matter in pounds, 



8 = distance in feet, 



T <= time in seconds, 



2'' = force in pounds. 

 (Whether these are the same pounds as men- 

 tioned above or other pounds seems to be of no 

 importance.) 



y = velocity in micro-speedals, 



A = acceleration in " gravitals," 

 and a> /?, y, 8, etc., be numerical constants of 

 proportionality. We may write the following 

 equations : 



V = aS/T, (1) 



A=^V/T:=apS/2P = yS/r-, 



(2) 



where it is understood that V in equation (2) 

 is a change in velocity and therefore twice the 

 average velocity defined by (1). (Initial 

 velocity being zero.) 



F = SWA=pSWV/T^ySWS/'P. (3) 



From these three fundamental equations we 

 may derive equations such as 



FT — ydWS/T={yS/a)WV^eWr (4) 

 and 



FS = ydWS~-/P = y8WV^ = ^WVK (5) 



And from these, as soon as we have established 

 units for momentum M, energy E, impulse I 

 and work Z, and determined the constants in 

 equations like I = r]FT and M=.6WV, we 

 could derive the equations of momentum and 

 of energy. 



The values of the constants may be easily 

 computed. Since one micro-speedal is 1,182.9 

 feet per second, a =■ 1,182.9. The equation 

 for an acceleration of one foot per second per 

 second is 



32.1740 1182.9?" 



which gives us at once 



32.1740 

 1182.9 



= .027200. 



